Problem: Reduce to lowest terms: $- \dfrac{4}{3} \div \dfrac{6}{5} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{6}{5}$ is $ \dfrac{5}{6}$ Therefore: $ - \dfrac{4}{3} \div \dfrac{6}{5} = - \dfrac{4}{3} \times \dfrac{5}{6} $ $ \phantom{- \dfrac{4}{3} \times \dfrac{5}{6}} = \dfrac{-4 \times 5}{3 \times 6} $ $ \phantom{- \dfrac{4}{3} \times \dfrac{5}{6}} = \dfrac{-20}{18} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{-20}{18} = \dfrac{-20 \div 2}{18 \div 2} = -\dfrac{10}{9} $